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Proof step 5 from proof unique-01 (previous step)

unique_al((p ' + ax0) + (a × d)'), unique_al(p ' + ax0), ∀ a0, d0. ¬ unique_al(ax0 + (a0 × d0)') ∨ ¬ unique_al(ax0) ∨ ¬ a0 ∈ ax0, a ∈ p ' ∨ a ∈ ax0 ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 6:
unique_al((a0 × d0)' + ax0), unique_al(((a0 × d0)' + ax0) + (a × d)'), ∀ a0, d0. ¬ unique_al(ax0 + (a0 × d0)') ∨ ¬ unique_al(ax0) ∨ ¬ a0 ∈ ax0, a ∈ (a0 × d0)' ∨ a ∈ ax0 ⊦

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;